As a general rule, you _must_ kiss her by the second date if you expect to have a serious relationship. Doesn't have to be a hot & heavy makeout. Can be a little peck at the end of the date.
But I'm firmly convinced that you _must_ kiss her by the second date.
First, if you want her to be your girlfriend you've got to behave like a boyfriend. And boyfriends want to kiss their girlfriends. Guys end up in the friend zone _only_ when they act like a friend, not a boyfriend. If you _don't_ kiss her by the second date, she may conclude that you're not interested in romance. If you _don't_ kiss her, she may lose interest, because women generally expect men to initiate.
Second, the kiss will help determine her intentions. By the time women are your age, they're probably (fairly) comfortable with kissing a date. Again, it doesn't have to be a deep, intense kiss. But if a girl is interested in you as a boyfriend, she will probably be willing and eager to kiss you by the second date. If she's unwilling to kiss you by the second date, that's often a red flag about her behavior and intentions.
These two rules aren't foolproof, of course, and there are always exceptions. But they're generally reliable as rules-of-thumb.